An Automatic Optimization Technique for the Calibration of a Physically Based Hydrological Rainfall-Runoff Model

Abstract

Models are tools widely used in the prediction of hydrological phenomena. The present study aims to contribute to the implementation of an automatic optimization strategy of parameters for the calibration of a hydrological model based on the least action principle (HyMoLAP). The Downhill Simplex method is also known as the Nelder-Mead algorithm, which is a heuristic research method, is used to optimize the cost function on a given domain. The performance of the model is evaluated by the Nash Stucliffe Efficiency Index (NSE), the Root Mean Square Error (RMSE), the coefficient of determination (R2 ), the Mean Absolute Error (MAE). A comparative estimation is conducted using the Nash-Sutcliffe Modeling Efficiency Index and the mean relative error to evaluate the performance of the optimization method. It appears that the variation in water balance parameter values is acceptable. The simulated optimization method appears to be the best in terms of lower variability of parameter values during successive tests. The quality of the parameter sets obtained is good enough to impact the performance of the objective functions in a minimum number of iterations. We have analyzed the algorithm from a technical point of view, and we have carried out an experimental comparison between specific factors such as the model structure and the parameter’s values. The results obtained confirm the quality of the model (NSE = 0.90 and 0.75 respectively in calibration and validation) and allow us to evaluate the efficiency of the Nelder-Mead algorithm in the automatic calibration of the HyMoLAP model. The developed hybrid automatic calibration approach is therefore one of the promising ways to reduce computational time in rainfall-runoff modeling.